Controlled flight of a multicopter experiencing a failure affecting an effector

ABSTRACT

According to a first aspect of the invention, there is provided a method for operating a multicopter experiencing a failure during flight, the multicopter comprising a body, and at least four effectors attached to the body, each operable to produce both a torque and a thrust force which can cause the multicopter to fly when not experiencing said failure. The method may comprise the step of identifying a failure wherein the failure affects the torque and/or thrust force produced by an effector, and in response to identifying a failure carrying out the following steps, (1) computing an estimate of the orientation of a primary axis of said body with respect to a predefined reference frame, wherein said primary axis is an axis about which said multicopter rotates when flying, (2) computing an estimate of the angular velocity of said multicopter, (3) controlling one or more of said at least four effectors based on said estimate of the orientation of the primary axis of said body with respect to said predefined reference frame and said estimate of the angular velocity of the multicopter. The step of controlling one or more of said at least tour effectors may be performed such that (a) said one or more effectors collectively produce a torque along said primary axis and a torque perpendicular to said primary axis, wherein (i) the torque along said primary axis causes said multicopter to rotate about said primary axis, and (ii) the torque perpendicular to said primary axis causes said multicopter to move such that the orientation of said primary axis converges to a target orientation with respect to said predefined reference frame, and (b) such that said one or more effectors individually produce a thrust force along said primary axis.

FIELD OF THE INVENTION

The present invention relates to the control of a multicopterexperiencing a failure affecting an effector. In particular, theinvention relates to a novel scheme for controlled flight that enablestranslational motion control of a multicopter by causing it to rotateand applying a novel control method, allowing the invention to be usedas a failsafe control mechanism in case of effector failure inconventional hover-capable aerial vehicles equipped with multiplerigidly-attached fixed-pitch propellers (“multicopters”).

BRIEF SUMMARY

In accordance with the present invention, limitations of previousmethods for the control of multicopters have been substantially reducedor eliminated. In particular, it provides a flying vehicle controlscheme for vehicles with as few as one functioning effector. Inaddition, it provides improved systems and methods for the control offlying vehicles in case of a failure affecting one or more effectors.

Technical advantages of certain embodiments of the present invention mayallow to improve or simplify the design of existing multicopters. Forexample, multicopters may require less mass and face fewer designconstraints and inherent limitations than current systems such as thosethat rely on effector redundancy (e.g., hexacopters and octocopters), oron the encasing of effectors (e.g., shrouds, ducted fans), or onparachutes as a safety backup.

Technical advantages of certain embodiments of the present invention mayallow to increase the safety and reliability of existing multicopters.For example, the present invention may allow to minimize or eliminaterisks inherent in such vehicles arising from collisions, mechanical orelectrical failures, electronic malfunctions, operator errors, oradverse environmental conditions, such as wind or turbulence. Thepresent invention may also mitigate the effects of failures,malfunction, operator errors, and the like by allowing for gracefuldegradation of performance rather than catastrophic failure withcomplete loss of control.

Other technical advantages of certain embodiments of the presentinvention may allow the use of multicopters for new applications byincreasing the reliability and safety of multicopters, by allowing theiruse in a wider variety of operating conditions and environments, or byallowing partial or full automation of certain tasks currently performedby experienced human pilots with both manned and unmanned flyingvehicles. The need for human pilots severely limits thecost-effectiveness, possible operating conditions, and flight enduranceof multicopters in many applications. For example, even experiencedhuman pilots cannot guarantee safe and efficient control in manyreal-world operating conditions including wind and turbulence.

Yet other technical advantages of certain embodiments of the presentinvention may allow it to be tailored to the specific needs of a varietyof applications in a variety of contexts. Example applications includeinspection and monitoring of civil infrastructure, which may requiredangerous or repetitive tasks; industrial or public service applications(e.g., surveillance and monitoring of industrial sites, photogrammmetry,surveying); professional aerial photography or cinematography; transportor delivery of cargo by air; or toys such as small flying vehicles;stage performances including choreographies set to music and light ortheater performances which require interaction with theater actors;hobbyist platforms for communities such as DIY Drones; researchplatforms for groups actively researching flying platforms or using themas part of their curriculum; military use with requirements such assurvivability, power autonomy, detectability, or operation in extremeconditions (weather, lighting conditions, contamination). In particular,certain technical advantages allow the present invention to be equippedwith a wide range of sensors. For example, infrared sensors allowembodiments for detection of patches of dry ground in orchards or forcrop monitoring.

According to a first, aspect, of the invention, there is provided amethod for operating a multicopter experiencing a failure during flight,the multicopter comprising a body, and at least four effectors attachedto the body, each operable to produce both a torque and a thrust forcewhich can cause the multicopter to fly when not experiencing saidfailure. The method may comprise the step of identifying a failurewherein the failure affects the torque and/or thrust force produced byan effector, and in response to identifying a failure carrying out thefollowing steps, (1) computing an estimate of the orientation of aprimary axis of said body with respect to a predefined reference frame,wherein said primary axis is an axis about which said multicopterrotates when flying, (2) computing an estimate of the angular velocityof said multicopter, (3) controlling one or more of said at least foureffectors based on said estimate of the orientation of the primary axisof said body with respect to said predefined reference frame and saidestimate of the angular velocity of the multicopter. The step ofcontrolling one or more of said at least four effectors may be performedsuch that (a) said one or more effectors collectively produce a torquealong said primary axis and a torque perpendicular to said primary axis,wherein (i) the torque along said primary axis causes said multicopterto rotate about said primary axis, and (ii) the torque perpendicular tosaid primary axis causes said multicopter to move such that theorientation of said primary axis converges to a target orientation withrespect to said predefined reference frame, and (b) such that said oneor more effectors individually produce a thrust force along said primaryaxis.

The torque is that torque about the multicopter's center of mass.

The angular velocity is preferably the velocity at which the themulticopter rotates with respect to an inertial frame.

Preferably, the step of controlling one or more of said at least foureffectors, based on said estimate of the orientation of the primary axisof said body with respect to the predefined reference frame and saidestimate of the angular velocity of the multicopter, comprisescontrolling said others of the at least four effectors not affected by afailure.

The torque and thrust are preferably a non-zero torque and a non-zerothrust.

Preferably, the torque and thrust force produced by each effector areinevitably, and intrinsically, linked.

Preferably, a component of the torque can be due to the effector thrustacting at a distance from the multicopter's center of mass. Anadditional component of the torque could be from a torque couplegenerated by the effector itself, for example due to aerodynamic effectson a rotating propeller.

In the present invention the primary axis need not be identical to aprinciple axis of inertia of the multicopter body.

Preferably, the primary rotation can at least be primarily created bythe remaining effectors not affected by the failure. Specifically, bythe component of the torques acting along the primary axis.

Preferably, the target orientation with respect to a predefinedreference frame can be freely selected, and the target orientation canbe both attained d and maintained.

The target orientation with respect to a predefined reference frame canbe thought of more specifically as a target orientation angle betweenthe primary axis and the direction of gravity, or the vertical directionin an inertial frame.

Preferably the target orientation can be freely selected at run time,preferably from a range, or specified list, of target orientations.

Although in principle unbounded, typical target orientations would be inthe range 0 degrees to 75 degrees, or more specifically, 0 degrees to 45degrees from the direction opposite to gravity.

The azimuthal direction of the target orientation can be anywhere in therange of 0 degrees to 360 degrees.

An effector failure can specifically mean a substantial reduction in theeffector's ability to produce a thrust force.

Such a failure could typically mean that the effector retains theability to produce between 0% and 50% of its original capacity toproduce thrust.

More specifically, it could be between 0% and 10% of the originalcapacity to produce thrust.

Failure can be caused by a variety of factors, including mechanicaldecoupling of an effector from the multicopter.

In case some effectors can no longer produce any thrust after thefailure occurs, the effectors producing thrust along the primary axiscould be all effectors not affected by the failures (e.g. if the failureis a motor falling off, all effectors for which the motor has not fallenoff would produce thrust along the primary axis).

The method may further comprise the step of controlling one or more ofsaid at least four effectors, based on (a) said estimate of theorientation of the primary axis of said body with respect to thepredefined reference frame and (b) said estimate of the angular velocityof the multicopter, such that said thrust force produced along saidprimary axis by each of said one or more effectors which are without afailure is at least 20% or 30% of the thrust collectively produced bysaid one or more effectors which are without a failure when theorientation of said primary axis has converged to said targetorientation.

The method may further comprise the step of identifying a failureaffecting the torque and/or thrust force produced by an effector, wherethe failure causes the torque and/or thrust, force produced by at leastone of said effectors to decrease by an amount greater than 20%, 50%, or80%, or wherein the failure causes a complete loss of the torque and/orthrust force of at least one of said effectors.

Failures can be detected using a great variety of methods, includingmonitoring by a human; indirect detection such as monitoring measureddata with an automatic method such as a model-based observer on oroff-board the multicopter, or using sliding mode observers, voting-basedalgorithms, parity-space approaches, or parameter identification; directdetection of the failure e.g. by monitoring the rotational speed of amulticopter's motors, or by monitoring how much current a multicopter'smotors draw; and others.

In the invention, it may furthermore be that said torque along saidprimary axis can cause said multicopter to rotate about said primaryaxis at a speed greater than 0.5 revolutions per second.

In the invention, it may furthermore be that said torque along saidprimary axis can cause said multicopter to rotate about said primaryaxis at a speed greater than 1 revolutions per second.

Preferably said torque along said primary axis can cause saidmulticopter to rotate continuously when the orientation of the primaryaxis has converged to the target orientation.

Preferably, said 0.5 or 1 revolutions per second are average rotationalspeeds during a predefined time interval.

Preferably, the target force is the sum of forces of the remaining,failure-free effectors.

The method may further comprise the step of defining a targetacceleration for said multicopter. Preferably said target accelerationis used to compute said target orientation of said primary axis for saidmulticopter. Preferably it additionally comprises the step ofcontrolling one or more of said at least four effectors, and preferablyadditionally comprises the step of controlling said one or moreeffectors so that the thrust collectively produced by said one or moreeffectors accelerates said multicopter at said target acceleration.

The method may further comprise the step of computing said targetorientation of said primary axis using said target acceleration of saidmulticopter, using the equation

$\overset{\sim}{n} = \frac{\left( {a - g} \right)}{{a - g}}$

wherein the vector a represents said target acceleration and the vectorg represents the gravitational acceleration, and the vector n representssaid target orientation, and ∥⋅∥ represents the Euclidean norm of avector. In other words, the target orientation of said primary axis canbe computed as the difference between the vector equaling said targetacceleration and the vector of gravitational acceleration, divided bythe Euclidean norm of that difference.

The method may further comprise the step of defining a target thrustforce magnitude. Preferably said step of controlling one or more of saidat least four effectors, based on said estimate of the orientation ofthe primary axis of said body with respect to the predefined referenceframe and said estimate of the angular velocity of the multicoptercomprises controlling said one or more effectors such that the magnitudeof the sum of each of said thrust forces produced individually by saidone or more effectors along said primary axis equals said target thrustforce magnitude.

In the invention, the method may further comprise the step of defining atarget thrust force magnitude. Preferably said step of controlling oneor more of said at least four effectors based on said estimate of theorientation of the primary axis of said body with respect to thepredefined reference frame and said estimate of the angular velocity ofthe multicopter comprises controlling said one or more effectors suchthat the magnitude of the sum of each of said thrust forces producedindividually by said one or more effectors along said primary axisaveraged over a predefined time period equals said target thrust forcemagnitude.

In the invention, the method may further comprise the step ofcontrolling one or more of said at least four effectors, preferablycomprising controlling each of said one or more of said at least foureffectors to each contribute at least 20% to the target thrust forcemagnitude when the orientation of said primary axis has converged tosaid target orientation.

In the invention, the method may further comprise the step of computingsaid target thrust force magnitude using said target acceleration ofsaid multicopter preferably comprising the steps of defining said targetacceleration, computing said target thrust force magnitude as

f _(des) =m∥a−g∥

wherein f_(des) represents the target thrust force magnitude, ∥⋅∥represents the Euclidean norm of a vector, a represents the said targetacceleration, g represents the acceleration due to gravity and nmrepresents the mass of said multicopter. In other words, the targetthrust force magnitude can be computed as the mass of said multicoptertimes the Euclidean norm of the difference between the vector equalingsaid target acceleration and the vector of gravitational acceleration.

Said controlling the acceleration may, for example, allow to control thedirection with which a multicopter collides with the ground following asevere failure that no longer allows the effectors to produce enoughthrust to keep the multicopter airborne.

In the invention, the method may further comprise the steps of defininga target translational velocity of said multicopter, defining a targetposition of said multicopter, estimating the current translationalvelocity of said multicopter, estimating the current position of saidmulticopter; and using at least one of said target translationalvelocity, said target position, said current translational velocity andsaid current position of said multicopter, to compute said targetacceleration.

Preferably the method uses the current translational velocity to computesaid target acceleration.

Preferably the method uses the current position to compute said targetacceleration.

Preferably, said method uses all of said target translational velocity,said target position, said current translational velocity and saidcurrent position of said multicopter to compute said targetacceleration.

A preferable method for how these estimates could be used would be asfollows. Let v_(des) and p_(des) represent the target velocity andposition of the multicopter, respectively, and let v and p represent theestimates of the current velocity and current position of themulticopter, respectively, and define the target acceleration asa_(des). If the multicopter tracks this target, acceleration, themulticopter's position and velocity will converge to the target if thetarget acceleration is selected as follows:

a _(des)+2ζω_(n)(v−v _(des))+ω_(n) ²(p−p _(des)),

wherein the parameter ζ represents a damping ratio, and ω_(n) representsa natural frequency, with both ζ and ω_(n) design parameters. A typicalchoice would be something similar to ζ=0.7 and ω_(n)=2rad/s. Note thatthe above equation is just one method for parametrising the targetacceleration in terms of the current and target position and velocity,with many others apparent to a person skilled in the arts, given thebenefits of the present invention.

Said controlling the velocity may allow, for example, to minimize theenergy of a multicopter when colliding with the ground following asevere failure that no longer allows the effectors to produce enoughthrust to keep the multicopter airborne.

For example, by making the target position constant, and moving themulticopter to this position (e.g., by controlling its acceleration),the multicopter can be in a hover state, where ‘hover’ here is used tomean remaining substantially at one point in space.

Preferably, the multicopter is a quadrocopter. In the presentapplication, a quadrocopter means a multicopter with four effectors,wherein each of said effectors is

-   -   rigidly attached to a body of the multicopter,    -   equipped with fixed-pitch propeller blades whose rotor pitch        does not vary as the blades rotate.    -   operable to produce both a torque and a thrust force, and    -   structured and arranged to contribute a thrust force which can        cause the multicopter to fly.

In the invention, it may furthermore be that each of said one or moreeffectors can individually produce a torque which has a non-zerocomponent along said primary axis.

In the invention, said controlling may furthermore comprise controllinga single variable of a plurality of variables of each of one or more ofsaid at least four effectors, wherein said plurality of variablescomprises at least one of

-   -   rotational speed,    -   voltage,    -   electric current,    -   fuel flow,    -   motor torque,    -   mass flow,    -   power.

Preferably, the single variable is a scalar value, e.g. a magnitude, andnot a vector. Furthermore, said single variables can also be consideredas signals such as effector control signals.

Preferably, the single variable sets both the thrust force and thetorque, simultaneously.

Preferably, to cause the orientation of the primary axis to converge toa target orientation, and while the multicopter has an ongoing rotationabout the primary axis, the multicopter body can be turned about aturning axis (preferably at a non-zero angle with respect to the primaryaxis). The effect of the two components of rotation, by Euler'sequations of motion governing the evolution of the angular velocity of arigid body, can preferably be exploited to create an angularacceleration (and thus velocity) linearly independent of the primaryrotation as well as the rotation about the turning axis.

Therefore, even if the effectors can not produce sufficient torque in adirection perpendicular to the primary axis, the present inventionallows to exploit this coupling effect inherent in the attitude dynamicsto achieve full attitude control. This is particularly relevant anduseful for the case of a multicopter with only one or two failure-freeeffectors.

In this present invention, attitude control means using a control unitto control the orientation of a primary axis of said multicopter.

For a propeller, a torque couple exists that produces a torque opposingthe propeller's rotation, due to air resisting the motion of thepropeller blades. This can contribute to the torque component in thedirection of the primary axis.

In the invention, said controlling may furthermore comprise controllingat most three of said at least four effectors.

In the invention, said controlling may furthermore comprise controllingat most two of said at least four effectors.

In the invention, said controlling may furthermore comprise controllingat most one of said at least four effectors.

According to a further aspect of the present invention there is provideda multicopter, comprising (A) a body, (B) at least four effectorsattached to the body, each operable to produce both a torque and athrust force which can cause the multicopter to fly when notexperiencing a failure, and a flight module configured such that it cancarry out a method for operating said multicopter experiencing a failureduring flight. The method may comprise the step of identifying a failurewherein the failure affects the torque and/or thrust force produced byan effector, and in response to identifying a failure carrying out thefollowing steps, (1) computing an estimate of the orientation of aprimary axis of said body with respect to a predefined reference frame,wherein said primary axis is an axis about which said multicopterrotates when flying, (2) computing an estimate of the angular velocityof said multicopter. (3) controlling one or more of said at least foureffectors based on said estimate of the orientation of the primary axisof said body with respect to said predefined reference frame and saidestimate of the angular velocity of the multicopter. The step ofcontrolling one or more of said at least four effectors may be performedsuch that. (a) said one or more effectors collectively produce a torquealong said primary axis and a torque perpendicular to said primary axis,wherein (i) the torque along said primary axis causes said multicopterto rotate about said primary axis, and (ii) the torque perpendicular tosaid primary axis causes said multicopter to move such that theorientation of said primary axis converges to a target orientation withrespect to said predefined reference frame, and (b) such that said oneor more effectors individually produce a thrust force along said primaryaxis.

Preferably, the multicopter's flight module comprises (1) an input unitfor receiving data from sensors and/or users, (2) a sensing unit forsensing the motion of said multicopter and/or the operation of at leastone of said effectors. (3) an evaluation unit operationally connected tosaid sensing and/or input unit for identifying a failure affecting thetorque and/or thrust force produced by one of said effectors, and (4) acontrol unit. Preferably, the control unit is configured to beoperationally connected to said evaluation unit, and is configured

-   -   to compute an estimate of the orientation of a primary axis of        said body with respect to a predefined reference frame, wherein        said primary axis is an axis about which said multicopter        rotates when flying under the control of said control unit; and    -   to send control signals to one or more of said effectors so        that, (a) the said one or more effectors collectively produce a        torque along said primary axis and a torque perpendicular to        said primary axis, wherein (i) the torque along said primary        axis causes said multicopter to rotate about said primary axis,        and (ii) the torque perpendicular to said primary axis causes        said multicopter to move such that the orientation of said        primary axis converges to a target orientation with respect to        said predefined reference frame, and (b) each of said one or        more of said at least four effectors individually produce a        thrust force along said primary axis.

Said evaluation unit may be configured to provide data representative ofthe motion of said multicopter, and may be operationally connected tosaid control unit to provide said data, and said control unit may beconfigured to perform controlling of said one or more effectors based onsaid results of said evaluation unit.

Said computation of the primary axis may be performed in dependence ofdata representative of the motion of said multicopter, and datarepresentative of the physical characteristics of said multicopter.

Preferably, said data representative of the motion of the multicoptercomprises at least one of an orientation of said multicopter, an angularvelocity of said multicopter, an operational state of said effectors ofsaid multicopter, an acceleration of said multicopter, a translationalvelocity of said multicopter or a position of said multicopter.Preferably said data representative of the physical characteristics ofsaid multicopter comprises at least one of the moments of inertia, mass,dimensions, aerodynamic properties or effector properties. Said datarepresentative of the physical characteristics are preferably stored ona memory unit. Said computation is preferably carried out on amicrocontroller.

Preferably, said control unit can be configured to control said one ormore effectors not affected by said failure such that each of said oneor more effectors contribute at least 20% of the thrust collectivelyproduced by said one or more effectors when the orientation of saidprimary axis has converged. Preferably, these one or more effectors areeffectors not affected by said failure.

Preferably, said control unit may be configured to control said one ormore effectors not affected by said failure such that each contribute atleast 30% of the thrust collectively produced by said one or moreeffectors when the orientation of said primary axis has converged.Preferably, these one or more effectors are effectors not affected bysaid failure.

Preferably, the evaluation unit is operable to identify a failure,wherein the failure causes the torque and/or thrust force produced by atleast one of the effectors to decrease by an amount greater than 20%.

Preferably, the evaluation unit is operable to identify a failure,wherein the failure causes the torque and/or thrust force produced by atleast one of the effectors to decrease by an amount greater than 50%.

Preferably, the evaluation unit is operable to identify a failure,wherein the failure the torque and/or thrust force produced by at leastone of the effectors to decrease by an amount greater than 80%.

Preferably, the evaluation unit is operable to identify a failure,wherein the failure causes a complete loss of the torque and/or thrustforce produced by at least one of said effectors.

Preferably, the evaluation unit uses a microprocessor.

Preferably, the evaluation unit identifies the failure based on datarepresentative of at least one of (a) one or more variables of aplurality of variables of the effector, wherein the plurality ofvariables of the effector comprises at least one of rotational speed,voltage, electric current, fuel flow, motor torque, mass flow, power; or(b) data representative of the motion of said multicopter, comprising anorientation of said multicopter, an angular velocity of saidmulticopter, an operational state of said effectors of said multicopter,an acceleration of said multicopter, a translational velocity of saidmulticopter or a position of said multicopter.

Said control unit may further be configured such that it can control atleast one of said effectors such that said one or more effectors maycollectively produce a torque along said primary axis to cause saidmulticopter to rotate about said primary axis at a speed greater than0.5 revolutions per second.

Preferably, said control unit is configured such that it can control atleast one of said effectors such that said one or more effectors maycollectively produce a torque along said primary axis to cause saidmulticopter to rotate about said primary axis at a speed greater than 1revolutions per second.

Preferably said torque along said primary axis can cause saidmulticopter to rotate continuously when the orientation of the primaryaxis has converged to the target orientation.

Preferably, said 0.5 or 1 revolutions per second are average rotationalspeeds during a predefined time interval.

Said control unit may further be configured to control a single variableof a plurality of variables of each of one or more of said at least foureffectors, wherein said plurality of variables comprises at least one of

-   -   rotational speed,    -   voltage,    -   electric current,    -   fuel flow,    -   motor torque,    -   mass flow,    -   power.

Preferably, the multicopter, after experiencing a failure wherein thefailure affects the torque and/or thrust force produced by an effector,comprises no more than three effectors unaffected by said failure.

Preferably, the multicopter, after experiencing a failure wherein thefailure affects the torque and/or thrust force produced by an effector,comprises no more than two effectors unaffected by said failure.

Preferably, the multicopter, after experiencing a failure wherein thefailure affects the torque and/or thrust force produced by an effector,comprises no more than one effector unaffected by said failure.

Said control unit may be further configured (a) to define a targetacceleration for said multicopter, and (b) to use said targetacceleration to compute said target orientation of said primary axis forsaid multicopter, and (c) to send said control signals such thatfurthermore said at least four effectors are controlled such that thethrust collectively produced by said one or more effectors acceleratessaid multicopter at said target acceleration.

Preferably, said target acceleration can be freely selected at run time,preferably from a range or specified list of target accelerations.

Preferably, said control unit is further configured to compute saidtarget orientation of said primary axis using said target accelerationof said multicopter by computing said target orientation using theequation

$\overset{\sim}{n} = \frac{\left( {a - g} \right)}{{a - g}}$

wherein the vector a represents said target acceleration and the vectorg represents the gravitational acceleration, and the vector ñ representssaid target orientation, and ∥⋅∥ represents the Euclidean norm of avector. In other words, the target orientation of said primary axis canbe computed as the difference between the vector equaling said targetacceleration and the vector of gravitational acceleration, divided bythe Euclidean norm of that difference.

Said control unit may further be configured to (a) define a targetthrust force magnitude, and (b) send said control signals such that themagnitude of the sum of each of said thrust forces produced individuallyby said one or more effectors along said primary axis equals said targetthrust force magnitude. Preferably, these thrust forces are produced byeffectors not affected by said failure.

Said control unit may further be configured to (a) define a targetthrust force magnitude, and (b) send said control signals such that themagnitude of the sum of each of said thrust forces produced individuallyby said one or more effectors along said primary axis over a predefinedtime period equals said target thrust force magnitude. Preferably, thesethrust forces are produced by effectors not affected by said failure.

Preferably, said target thrust force magnitude can be freely selected atrun time, preferably from a range or specified list of target thrustforce magnitudes.

Said control unit may further be configured to compute said targetthrust force magnitude using said target acceleration of saidmulticopter by (a) defining said target acceleration, and (b) computingsaid target thrust force magnitude as

f _(des) =m∥a−g∥

wherein f_(des) represents the target thrust force magnitude, ∥⋅∥represents the Euclidean norm of a vector, a represents the said targetacceleration, g represents the acceleration due to gravity and inrepresents the mass of said multicopter. In other words, the targetthrust force magnitude can be computed as the mass of said multicoptertimes the Euclidean norm of the difference between the vector equalingsaid target acceleration and the vector of gravitational acceleration.

Said multicopter may further comprise a sensor which may beoperationally connected to said sensing unit and configured to (a)detect data representative of the motion of the multicopter, and (b)provide said data representative of the motion of the multicopter tosaid sensing unit. Preferably, the sensor belongs to the group ofinertial sensors, distance sensors, or rate sensors. Preferably, thesensor belongs to the group of accelerometers, gyroscopes,magnetometers, cameras, optical flow sensors, laser or sonar rangefinders, radar, barometers, thermometers, hygrometers, bumpers, chemicalsensors, electromagnetic sensors, air flow sensors or relative airspeedsensors, ultra sound sensors, microphones, radio sensors, or otherheight, distance, or range sensors, or infra-red sensors.

Said multicopter may further comprise a sensor which is arranged todetect data representative of the operation of at, least one of saideffectors, and operationally connected to, and providing said datarepresentative of the operation of at least one of said effectors, tosaid sensing unit.

Preferably the sensor uses at least one of a single variable of aplurality of variables of the effector, wherein the plurality ofvariables of the effector comprises at least one of a rotational speed,a voltage, electric current, fuel flow, motor torque, mass flow, power.

Said control unit, may be mechanically independent of said body and saidat least four effectors, and operationally connected to the multicoptervia a wireless connection. Such a wireless connection may consist of aWiFi connection, Bluetooth. ZigBee, or another type of radio connection.Alternatively, the connection could consist of an optical connection,e.g. consisting of infrared transmissions.

Preferably, said mechanically independent control unit is contained in ahousing, structured and arranged to be held in the hand of a user, andconfigured to receive input from said user via a user interface usableto control one or more of said at least four effectors of saidmulticopter via said wireless connection. Such a handheld device couldbe in the form of a smartphone, or a tablet computer device, or it,could be in the form similar to traditional hobbyist remote controllers.

According to a further aspect of the present invention there is provideda control unit for a multicopter, the multicopter comprising: (1) abody, (2) at least four effectors attached to the body, each operable toproduce both a torque and a thrust force which can cause the multicopterto fly when not experiencing a failure; and said control unit comprisinga flight module configured such that it can carry out a method foroperating said multicopter experiencing a failure during flight. Themethod may comprise the step of identifying a failure wherein thefailure affects the torque and/or thrust force produced by an effector,and in response to identifying a failure carrying out the followingsteps, (1) computing an estimate of the orientation of a primary axis ofsaid body with respect to a predefined reference frame, wherein saidprimary axis is an axis about which said multicopter rotates whenflying, (2) computing an estimate of the angular velocity of saidmulticopter, (3) controlling one or more of said at least four effectorsbased on said estimate of the orientation of the primary axis of saidbody with respect to said predefined reference frame and said estimateof the angular velocity of the multicopter. The step of controlling oneor more of said at least four effectors may be performed such that (a)said one or more effectors collectively produce a torque along saidprimary axis and a torque perpendicular to said primary axis, wherein(i) the torque along said primary axis causes said multicopter to rotateabout said primary axis, and (ii) the torque perpendicular to saidprimary axis causes said multicopter to move such that the orientationof said primary axis converges to a target orientation with respect tosaid predefined reference frame, and (b) such that said one or moreeffectors individually produce a thrust force along said primary axis.

Preferably, the control unit's flight module comprises (I) an input unitfor receiving data from sensors and/or users, (2) a sensing unit forsensing the motion of said multicopter and/or the operation of at leastone of said effectors, (3) an evaluation unit operationally connected tosaid sensing and/or input unit for identifying a failure affecting thetorque and for thrust force produced by one of said effectors, and (4) acontrol unit. Preferably, the control unit is configured to beoperationally connected to said evaluation unit, and is configured

-   -   to compute an estimate of the orientation of a primary axis of        said body with respect to a predefined reference frame, wherein        said primary axis is an axis about which said multicopter        rotates when flying under the control of said control unit; and    -   to send control signals to one or more of said effectors so        that, (a) the said one or more effectors collectively produce a        torque along said primary axis and a torque perpendicular to        said primary axis, wherein (i) the torque along said primary        axis causes said multicopter to rotate about, said primary axis,        and (ii) the torque perpendicular to said primary axis causes        said multicopter to move such that the orientation of said        primary axis converges to a target orientation with respect to        said predefined reference frame, and (b) each of said one or        more of said at least four effectors individually produce a        thrust force along said primary axis.

The control unit may be operationally connected to said evaluation unit,wherein said evaluation unit provides data representative of the motionof said multicopter, and provides said data to said control unit, andsaid control unit performs controlling of said one or more effectorsbased on said results of said evaluation unit.

The control unit may further be configured to compute a primary axis ofsaid body, wherein (a) said primary axis is an axis about which saidmulticopter rotates when flying under the control of said control unit,and (b) each of said one or more effectors produces a thrust force alongsaid primary axis, and wherein said computation of the primary axis isperformed in dependence of data representative of the motion of saidmulticopter, and data representative of the physical characteristics ofsaid multicopter.

Preferably, said data representative of the motion of the multicoptercomprises at least one of an orientation of said multicopter, an angularvelocity of said multicopter, an operational state of said effectors ofsaid multicopter, an acceleration of said multicopter, a translationalvelocity of said multicopter or a position of said multicopter.

Preferably said data representative of the physical characteristics ofsaid multicopter comprises at least one of the moments of inertia, mass,dimensions, aerodynamic properties or effector properties. Said datarepresentative of the physical characteristics are preferably stored ona memory unit. Said computation is preferably carried out on amicrocontroller.

According to yet another aspect of the present invention, there isprovided the use of said control unit for a multicopter, the multicoptercomprising (1) a body, (2) at least four effectors attached to the body,each operable to produce both a torque and a thrust force which cancause the multicopter to fly when not experiencing a failure; whereinsaid control unit comprises a flight module configured such that it cancarry out a method for operating said multicopter experiencing a failureduring flight. The method may comprise the step of identifying a failurewherein the failure affects the torque and/or thrust force produced byan effector, and in response to identifying a failure carrying out thefollowing steps, (1) computing an estimate of the orientation of aprimary axis of said body with respect to a predefined reference frame,wherein said primary axis is an axis about which said multicopterrotates when flying, (2) computing an estimate of the angular velocityof said multicopter, (3) controlling one or more of said at least foureffectors based on said estimate of the orientation of the primary axisof said body with respect to said predefined reference frame and saidestimate of the angular velocity of the multicopter. The step ofcontrolling one or more of said at, least four effectors may beperformed such that (a) said one or more effectors collectively producea torque along said primary axis and a torque perpendicular to saidprimary axis, wherein (i) the torque along said primary axis causes saidmulticopter to rotate about said primary axis, and (ii) the torqueperpendicular to said primary axis causes said multicopter to move suchthat the orientation of said primary axis converges to a targetorientation with respect to said predefined reference frame, and (b)such that said one or more effectors individually produce a thrust forcealong said primary axis.

Preferably, the control unit's flight module comprises (1) an input unitfor receiving data, from sensors and/or users, (2) a sensing unit forsensing the motion of said multicopter and/or the operation of at leastone of said effectors, (3) an evaluation unit operationally connected tosaid sensing and/or input unit for identifying a failure affecting thetorque and/or thrust force produced by one of said effectors, and (4) acontrol unit. Preferably, the control unit is configured to beoperationally connected to said evaluation unit, and is configured

-   -   to compute an estimate of the orientation of a primary axis of        said body with respect to a predefined reference frame, wherein        said primary axis is an axis about which said multicopter        rotates when flying under the control of said control unit; and    -   to send control signals to one or more of said effectors so        that, (a) the said one or more effectors collectively produce a        torque along said primary axis and a torque perpendicular to        said primary axis, wherein (i) the torque along said primary        axis causes said multicopter to rotate about said primary axis,        and (ii) the torque perpendicular to said primary axis causes        said multicopter to move such that the orientation of said        primary axis converges to a target orientation with respect to        said predefined reference frame, and (b) each of said one or        more of said at least four effectors individually produce a        thrust force along said primary axis.

Preferably, the failure affecting the torque and/or thrust forceproduced by one of said effectors causes said torque and/or thrust forceto decrease by an amount greater than or equal to 20%, 50%, 80%, or100%.

Other technical advantages of the present invention will be readilyapparent to one skilled in the art from those following figures,descriptions, and claims. Moreover over, while specific advantages havebeen enumerated above, various embodiments may include all, some, ornone of the enumerated advantages.

BRIEF DESCRIPTION OF THE DRAWINGS

For a more complete understanding of the invention, reference is made tothe following description and accompanying drawings, in which:

FIG. 1 shows a schematic of a first preferred embodiment of theinvention, showing a quadrocopter experiencing a failure disabling asingle effector, and nevertheless capable of controlled flight using thedisclosed method;

FIG. 2 shows a schematic of a failure-free quadrocopter as known in theprior art;

FIG. 3 shows a block diagram of a flight module and its parts;

FIG. 4 shows a schematic of a quadrocopter experiencing two rotorfailures and the torques and forces used to explain the derivation ofthe control method;

FIG. 5 shows a table with typical effector failures for a quadrocopterto illustrate the applicability of the present invention:

FIG. 6 shows a block diagram for explaining an exemplary controlarchitecture that can be used with the present invention;

FIG. 7 shows schematics of three alternative multicopters experiencingvarious effector failures, where each resulting configuration can becontrolled using the disclosed control method;

FIG. 8 shows a flowchart for deciding on a suitable control method incase of effector failure;

FIG. 9 shows a schematic of a quadrocopter with one failed effector,used to explain the derivation of the control method; and

FIG. 10 shows a schematic of a quadrocopter with three failed effectors,used to explain the derivation of the control method.

DETAILED DESCRIPTION

The disclosed invention relates to the control of motion of amulticopter experiencing a failure affecting one or more effectors.Multicopters are typically equipped to with effectors that produce botha thrust force and a torque acting on the multicopter. These effectorsare typically characterized by having a characteristic drive axis(typically identical to the direction of thrust force), which is fixedwith respect to the body of the multicopter, and by having a singlevariable which controls the thrust force. For example, the fixed-pitchpropellers used on many hover-capable aerial vehicles such asmulticopters produce a thrust force and torque acting on the vehicle,and are typically directly fixed to a motor's fixed drive axis andcommanded using a single variable. For multicopters, this singlevariable typically commands the relative desired speed of the motor andthus the thrust force of the effector. Multicopters typically usebrushless motors, which typically use a motor controller to convert thissingle variable into amplitude, waveform, and frequency required toachieve a desired rotor speed. Such motor controllers typically contain3 bi-directional outputs (i.e. frequency controlled three phase output),which are controlled by a logic circuit, but can have more compleximplementations involving additional sensors and electronics to achievehigh performance or other desirable properties. A hover-capable vehicleis a heavier-than-air flying vehicle that is able to approximatelyattain and maintain a position at a target point in space.

A defining characteristic of the present invention is that the disclosedcontrol scheme results in a continuous rotation of the multicopter abouta primary axis 130 defined in a coordinate system fixed with respect tothe body of the multicopter and passing through its center of mass. Onmulticopters, effectors are arranged in such a way that in addition toproviding a force along their drive axes, they also create a torqueacting on the multicopter's center of mass and with a componentperpendicular to the primary axis 130.

To achieve and sustain this rotation of the multicopter about, theprimary axis 130, the effectors can further be made to produce a torquewith a component in the direction of the primary axis 130. For afixed-pitch propeller, the torque component can be achieved by placingthe drive axis of the propeller parallel to the primary axis 130, andusing the aerodynamic reaction drag torque acting to oppose thepropeller's rotation (and thus acting in the direction of the primaryaxis 130).

In the present application, failure affecting an effector means apartial or complete loss of torque and/or thrust force produced by theeffector. Typically this loss is in the range of 20% to 100% of thenominal thrust. Overall, multicopters are comparably simple and hencecomparably safe flying vehicles (the best system on an aircraft is theone that it doesn't have, because it can never fail). However, due totheir enormous popularity, a very large number of multicopter crashesare documented in the literature. The vast majority of all multicoptercrashes are due to effector failure—apart, from pilot errors that resultin a collision of the multicopter with an obstacle, the multicoptertypically stays airborne as long as effectors do not fail at producingthrust in a controlled way. The present invention may therefore allow toovercome or limit, the consequences of the vast, majority of allmulticopter crashes, including some that involve collisions with anobstacle. The most common multicopter failures in the literature are:

-   -   1. Failures due to collisions with obstacles due to piloting        errors or wind or turbulence. For example, during an inspection        operation a sudden gust of wind pushes a multicopter into a        bridge, resulting in an effector failure due to a broken        propeller, and subsequent catastrophic loss of control and        crash.    -   2. Failures of a multicopter's wiring. Examples of very common        failures include:        -   Unplugging of a motor connector due to vibrations.        -   Detachment of a soldered wire.        -   Loose wire cut by a propeller.        -   Wire ripped off by partial motor attachment failure (shaking            lose of fastening screw or material fatigue of assembly).        -   Insufficient wire size and resulting overheating/melting of            wire or solder attachment point.    -   3. Failures of a multicopter's propeller attachment, motor        attachment or frame. The most common failures include:        -   Loose screws and bolts (loosened by vibrations, assembly            errors, wear-and-tear, material fatigue).        -   Propellers attached in wrong configuration            (counter-clockwise (sometimes called “puller” propellers)            and clockwise propellers (sometimes called “pusher”            propellers)).        -   Overtightening of attachment screws.        -   Undertightening of attachment screws.    -   4. Failures to properly balance all motors, to properly balance        all propellers, and failures due to bent motor collets and        shafts. This category is a main cause of vibrations and        subsequent dislodging of parts, especially on larger        multicopters.    -   5. Failures of a multicopter's motor. The most common failures        result from overloading of motors (e.g., too large propellers)        and subsequent overheating or operation in dust or sand.    -   6. Failures of a multicopter's electrical or electronic        components. The most common failure in this category is flight        in wet conditions such as rain, fog, or high humidity.    -   7. Failures of a multicopter's flight software. For example,        improper programming of the flight control computer or improper        motor gains for the aircraft weight.    -   8. Failures caused by improper remote control configurations, in        particular reversed or improperly configured transmitter        channels, or failure to ensure a strong enough signal between        base station and receiver.    -   9. Failures caused by interference, most commonly interference        between the electronic speed controls (also called “motor        controller”) with the multicopter's receivers.    -   10. Failures due to bad payloads.    -   11. Failures due to a lack of or faulty sensor calibration.    -   12. Failures of a propeller due to material fatigue (e.g.,        fatigue cracks or stress fractures).

While not all of the above failures directly result in an effectorfailure, many result in flight configurations that can be controlledusing the present invention. In particular, following one of the abovefailures, the present invention may allow to prevent a multicopter crashin spite of a loss of thrust by controlling the remaining effectors suchthat the multicopter enters a substantial continuous rotation around aprimary axis 130, and by using the method disclosed herein to attain ormaintain an orientation this primary axis 130 into a favorabledirection, allowing for a controlled descent and landing.

Various methods can be used to detect that a failure has occurred.Examples include having a pilot who monitors the multicopter, and whocan send a signal to the multicopter when a failure is observed, whichthen causes the multicopter to use the present invention to control themulticopter. Alternatively, the detection can be automatic, for exampleby having a model-based observer on the multicopter monitoring measureddata, and probabilistically detecting that an error has been observed(utilising, for example, a bank of Kalman filters where each representsa different failure mode). Sliding mode observers, voting-basedalgorithms, parity-space approaches, and parameter identification canalso be used. The failure might also be detected directly. e.g. bymonitoring the rotational speed of a multicopter's motors, or bymonitoring how much current a multicopter's motors draw.

Some failure detection methods might detect a failure only a certaintime after it has occurred, meaning that the multicopter might be in astate far from the intended when the failure is recognised. Certainevents, such as a collision with an obstacle, will also tend to put themulticopter in a state far away from the expected. Nonetheless, thedisclosed invention will allow the multicopter to recover from anarbitrary initial state. Depending on the specific multicopterconfiguration (such as mass, remaining effectors unaffected by thefailure, etc.) the multicopter might be able to return to a hover afterthe failure, or freely move around space. Alternatively, instead ofcontrolling the position, the disclosed invention could be used simplyto reorient the multicopter after a failure, such that it (e.g.) hitsthe ground in a favourable way.

The invention may also offer the possibility of reducing the severity ofpilot error. For example, if a pilot of a quadrocopter were toaccidentally collide the quadrocopter with a structure, and therebydamage one of the propellers, an automated system could detect that afailure has occurred, and that some of the multicopter's effectors havebeen affected by a failure. The system could then automatically engagean internal autopilot, utilising available sensors to bring themulticopter to a hover, or to bring the multicopter to a soft, landingon the ground.

FIG. 1 shows an exemplary arrangement, of a preferred embodiment for aquadrocopter 140 with three remaining working effectors 102, and oneeffector disabled by a failure 100, each effector in the form of afixed-pitch propeller 104 driven by a motor 106. The multicopter 140consists of effectors 102 and a body 112 comprising a mechanicalstructure 114. The mechanical structure 114 and multicopter body 112also house sensors, cabling, electronics, and other components of themulticopter (none shown). The multicopter's center of mass 120 is markedwith a bi-colored circle. The propellers 104 spin about parallel driveaxes of rotation 110, with the aerodynamic reaction drag torque of thepropellers 101 resulting in a continuous rotation 11S of the entiremulticopter body 112 about a primary axis 130. Two of the workingpropellers spin in one direction 108 b, while the third spins in theopposite direction 108 a. Although uncontrollable using the standardmulticopter control met hod as known in the prior art, the disclosedinvention can be applied to still control the multicopter, by causing itto spin about a primary axis 130 and controlling the orientation of thisprimary axis in a predefined reference frame 160. The figure also showsa target orientation of the primary axis 150, and a predefined referenceframe 160. The effectors 102 are individually numbered one 102 a, two102 b, three 102 c and four 102 d for convenience.

The orientation of the primary axis is typically estimated using analgorithm, allowing the calculation of an estimate of the orientation ofthe primary axis 150. Similarly, an estimate of the angular velocity ofthe multicopter can be computed. Examples of algorithms to compute theseestimates include Kalman filters and Luenberger observers. The locationof the multicopter in space is described by a position and tranlsationalvelocity, typically defined in a predefined reference frame 160 andreferred to some fixed point. Examples of a predefined reference frame160 would be a ‘East-North-Up’ frame, with the origin fixed to somelandmark. An estimate of the position, and an estimate of thetranslational velocity, of the multicopter can be computed by analgorithm similar to that of the orientation and angular velocity.

The motion of a flying vehicle is usually described by referring to aninertial reference frame. By neglecting the rotation of the Earth aboutits own axis, and about the sun, and the sun's rotation through themilky way, an Earth-fixed frame can be used as an approximation for aninertial reference frame. Thus, an Earth-fixed reference frame can beconstructed by letting a first axis point from West to East, a secondaxis point South to North, and the final axis pointing from the centerof the earth upward. Such a frame has proven to be a good approximationfor objects moving at low speeds and over short distances. For greateraccuracy, frames can be constructed with one direction pointing from thesun's center of gravity in a direction normal to the ecliptic plane (theplane through which the earth's center of mass moves as it rotates aboutthe sun), and a second direction pointing to the First Point of Aries(or the vernal equinox), with the third direction following from theright hand rule.

The operator of the multicopter often has some higher level goal, whichcan be translated into a target, acceleration for the multicopter, or atarget translational velocity, or a target position. Furthermore, somegoals might be translated into a target thrust force magnitude, wherethis is the desired total force produced by the multicopter's effectors.

FIG. 2 shows a failure-free quadrocopter as known in the prior art, withtwo pairs of rigidly attached, fixed-pitch propellers, one pair 108 arotating in the clockwise direction and the other pair 108 bcounterclockwise. Propellers typically have two, three, or four bladesand are sometimes also called “rotary wings” or “rotors” and defined toalso include all rotating parts of a motor used to move them.Multicopters are hover-capable multicopters with multiple propellers.Typical arrangements use four, six, or eight, propellers, which arecommonly referred to as quadrocopters, hexacopters, and octocopters,respectively, and are well known in the prior art and widely used.However, many variations including 16 and more propellers arranged inmany configurations (e.g., with aligned as well as inclined or invertedaxes; arranged individually or contra-rotating; exposed or encased inducts or protective shrouds) are in use. Multicopters typically usefixed-pitch blades whose rotor pitch does not vary as the blades rotatefor mechanical simplicity. This mechanical simplicity and the resultingease of construction, combined with high agility and the ability tomaintain position (hover) make multicopters the platform of choice formany aerial applications.

Multicopter motion is typically controlled via control signals sent tothe multicopter's effectors to vary the relative speed of each propellerto change the thrust and torque. The relative speed of each propeller istypically set using a single variable, which is translated into controlsignals by a motor controller. Translational motion in the direction ofthrust of the four propellers (sometimes “total thrust” or “collectivethrust”) is controlled by changing the individual thrusts of each of thepropellers to achieve the target total force. Independent of thecollective thrust, rotation about the direction of the total thrust(usually called “yaw”) is controlled by spinning up either the clockwiseor the counterclockwise propellers while respectively slowing down theother propellers, thereby producing a torque produced by the differenceof drag effects between the propellers rotating clockwise and thepropellers rotating counter-clockwise. Independently of the above,rotation about the other axes is controlled by using thrust differencebetween opposite propellers, while maintaining the independentrelationships described above to control yaw and total thrust asdesired. In total, four independent motion properties (“degrees offreedom”) of the multicopter, one translational and three rotational,are thus independently controlled by appropriately modulating thethrusts produced by the propellers. With some minor variation, thisprinciple of operation typically applies to all commonly usedmulticopter vehicles. Full translational control is then achieved byorienting the total force in the direction of desired translationalmotion.

FIG. 3 shows an example of a flight module for a multicopter that can beused as part of the disclosed control scheme. For multicopters, such aflight module is typically implemented on-board or both on-board andoff-board (e.g., with a control unit 306 directly connected with theon-board motors but also receiving inputs via an input unit 304 fromoff-board sensors via an off-board sensing unit 310 such as a cameratracking system). Flight modules are typically used to process vehicleinputs (e.g., user commands, sensor readings) and to compute outputs(e.g., control signal for effectors 314). For example, they allow activeself-stabilization by generating control outputs for the flighteffectors (e.g. the propellers 104) as well as for any other effectorsor actuators. In multicopters, flight modules are used in variousoperating modes including remote control by an operator with a directline of sight to the multicopter; controlled remotely by relaying sensordata to a pilot and relaying control signals back to the multicopter(sometimes referred to as “telepresence”); or in partial or fullyautonomous modes of operation.

Flight modules typically receive high level inputs in the form of goalsor commands from a user, base station, command center, or high levelcontrol algorithm via an input unit 304 and passed on to a control unit306, evaluation unit 308, and sensing unit 310. Control units 306 aretypically used to generate control signals for a multicopter'seffectors. Evaluation units 308 are typically used to evaluate data frominput units 304, sensing units 310, and memory units 312. Such data maybe representative of user commands or high level commands as well asboth relative or absolute position, particularly that of GPS sensors,visual odometry/SLAM, retro-reflective positioning systems, laser rangefinders, WiFi positioning systems, barometric altimeters andvariometers, or ultra-sound sensors (none shown). Sensor data may begathered and preprocessed using a sensor unit 310 or stored in a memoryunit 312. Typical examples of processed information are those receivedfrom sensors, such as accelerometers, gyroscopes, magnetometers,cameras, optical flow sensors, laser or sonar range finders, radar,barometers, thermometers, hygrometers, bumpers, chemical sensors,electromagnetic sensors, air flow sensors, or microphones (none shown).Memory units 312 are typically used to store data. For example, they maybe used to store data on past sensor readings, operational states oruser commands, as well as properties of the multicopter.

All of the above units may be implemented on a single circuit board, ona single board computer, or on a single microcontroller.

Depending on the application, flight modules may be far more complexthan the simple block diagram shown in FIG. 3 and may, in particular,comprise multiple input units 304, control units 306, evaluation units308, sensing units 310, and memory units 312 arranged in a single block302 or multiple blocks.

FIG. 4 (A) shows a quadrocopter with two opposing effectors disabled dueto a failure 100, and two remaining, working, effectors spinning in thesame sense 108 b. During hover operation and utilising the presentinvention, the forces and torques create a continuous rotation of themulticopter body about the primary axis 130. A coordinate system isdefined fixed with respect to the multicopter's body, consisting of thedirections z, y and z, where z is chosen for this case such that itcoincides with the primary axis 130, and x lies perpendicular to z andpoints from the center of mass 120 to the first effector, y follows fromthe right-hand-rule. The three instantaneous rates of rotation for themulticopter, p, q, r are defined about the multicopter body-fixed axesx, y, z, respectively.

As illustrated, the multicopter body has an instantaneous angularvelocity ω^(B), that is nominally aligned with the primary axis 130, butmay deviate in direction and magnitude during corrective or commandedmotion.

The rotation of this body fixed frame with respect to some inertialcoordinate frame is described by the rotation matrix R, governed by thedifferential equation

{dot over (R)}=R[[ω^(B) x]]  (1)

where ω^(B)=(p, q, r) is the angular velocity of the multicopter asshown with its components in FIG. 4(D), expressed in the coordinatesystem fixed to the multicopter body, and [[ω^(B)x]] is the matrix formof the cross product, such that

$\begin{matrix}{{〚{\omega^{R} \times}〛} = {\begin{bmatrix}0 & {- r} & q \\r & 0 & {- p} \\{- q} & p & 0\end{bmatrix}.}} & (2)\end{matrix}$

The orientation, or direction, z of the primary axis 130 in the inertialcoordinate frame, can be expressed as

$\begin{matrix}{{z = {R^{T}\begin{bmatrix}0 \\0 \\1\end{bmatrix}}},} & (3)\end{matrix}$

such that the differential equation of the orientation can be found with(1):

$\begin{matrix}{\overset{.}{z} = {{{R\begin{bmatrix}0 & {- r} & q \\r & 0 & {- p} \\{- q} & p & 0\end{bmatrix}}\mspace{11mu}\begin{bmatrix}0 \\0 \\1\end{bmatrix}} = {{R\begin{bmatrix}q \\{- p} \\0\end{bmatrix}}.}}} & (4)\end{matrix}$

From this follows that the primary axis 130 can be made to achieve acommanded orientation if the angular velocity components p and q can becontrolled, and will maintain an orientation if the components p and qare zero.

Each effector i has a single commandable degree of freedom (here alsoreferred to as a single variable), and produces a thrust force vectorf_(T) _(i) (FIG. 1(C)) and a torque vector τ_(i) about the multicopter'scenter of mass 120 (FIG. 4(B)), where the torque vector consists of themoment of the thrust force vector and includes aerodynamic reaction dragtorque acting to oppose the propeller's rotation. Additionally, themulticopter's weight mg acts on the multicopter, and there exists anaerodynamic drag torque τ_(d) acting to oppose the multicopter's angularvelocity.

The differential equation governing the evolution the angular velocityof a body with rotating effectors is given by

$\begin{matrix}{{I^{B}{\overset{.}{\omega}}^{B}} = {{\sum\limits_{j}\tau_{j}} - {{〚{\omega^{B} \times}〛}\mspace{11mu} {\left( {{I^{B}\omega^{B}} + {\sum\limits_{i}{I^{R_{i}}\left( {\omega^{B} + \omega^{R_{i}}} \right)}}} \right).}}}} & (5)\end{matrix}$

where ω^(R) ^(i) is the rotation rate vector of effector i, I^(B) is theinertia matrix of the multicopter body, expressed in the body-fixedcoordinate system; I^(R) ^(i) is the inertia matrix of effector i; andτ_(j) includes the torque vector of each rotor i acting through themulticopter's center of mass 120, and any other torques acting on themulticopter (such as aerodynamic drag torque on the multicopter). Notethat the inertia of the body is taken to include any components rigidlyattached to the body, such as the multicopter structure, control units,sensors.

The left side of (5) contains the angular accelerations {dot over (p)},{dot over (q)}; where control of these components allows the control ofthe orientation of the primary axis through (4). The first term of theright side of (5) is the sum of all the torques acting on themulticopter. The remaining term of (5) expresses the cross coupling ofthe angular momentum in the system, due to taking the derivative in anon-inertial frame.

FIG. 4(B) shows the torque vectors 7, produced by each of the tworemaining rotors on the multicopter's center of mass 120, and theircomponents perpendicular to the primary axis 130.

FIG. 4(C) shows the thrust force vectors f_(T) _(i) produced by each ofthe two remaining rotors on the multicopter's center of mass 120, andtheir components acting in the direction of the primary axis 130. Thefigure also shows the weight of the multicopter mg. By orienting themulticopter's primary axis 130, and through the sum of the propeller'sthrust force vectors, a total force is achieved. This total force can beoriented in a target direction by the mechanism of orienting the primaryaxis 130 as described above.

The translational acceleration is related to the total forces throughNewton's second law. Thus a translational acceleration of themulticopter can be effected through the total force, while thisacceleration, in turn, allows to effect a translational velocity, whichin turn allows to effect a change in the position of the multicopter.For the sake of clarity of exposition, the following assumptions aboutthe system are made for the derivation. Note that these assumptions arereasonable for the derivation of control schemes for practicalmulticopter configurations, and lead to practical and applicable controlschemes.

-   -   The mass distribution of the multicopter body is such that, the        principle axes of inertia coincide with x, y and z, such that        the inertia matrix I^(B) is diagonal,

$\begin{matrix}{I^{B} = {\begin{bmatrix}I_{X}^{B} & 0 & 0 \\0 & I_{Y}^{B} & 0 \\0 & 0 & I_{Z}^{B}\end{bmatrix}.}} & (6)\end{matrix}$

-   -   The effectors are propellers, mounted along the x axis of the        body, each at a distance of l from the multicopter's center of        mass 120.    -   The effectors are identical propellers, have a mass negligible        when compared to that of the quadrocopter, have a diagonal        inertia matrix I^(R) whose magnitude is negligible compared to        that of the multicopter body, and rotate around axes parallel to        the primary axis 130.

$\begin{matrix}{I^{R} = \begin{bmatrix}I_{X}^{R} & 0 & 0 \\0 & I_{Y}^{R} & 0 \\0 & 0 & I_{Z}^{R}\end{bmatrix}} & (7)\end{matrix}$

-   -   The magnitude of the angular velocity of the multicopter body is        negligible when compared to the magnitude of the angular        velocity of either propeller.    -   The force vectors produced by the propellers f_(T) _(i) , are        parallel, and parallel to the multicopter primary axis 130 as        illustrated in FIG. 4(C), such that they can be

$\begin{matrix}{f_{T_{i}} = \begin{bmatrix}0 \\0 \\f_{T_{i}}\end{bmatrix}} & (8)\end{matrix}$

(note the distinction between vector f_(T) _(i) and the scalar f_(T)_(i) . The only other force assumed to act on the multicopter is itsweight mg.

-   -   The components of the torque vectors produced by the propellers,        acting through the multicopter's center of mass 120 and        perpendicular to the primary axis 130, are colinear with and        parallel to y as illustrated in FIG. 4(B). It is assumed that        the component acting perpendicular to the primary axis 130 is        exclusively due to the moment of the propeller's thrust vector        force f_(T) _(i) acting at the distance 1 from the center of        mass 120, and that there is no torque component in the direction        of x. The component of the torque parallel to the primary axis        130 is τ_(i∥) and is caused by the aerodynamic reaction drag        torque to oppose the rotation of the propeller. Thus the        propellers' torque vectors expressed in the body fixed frame        are:

$\begin{matrix}{{\tau_{1} = \begin{bmatrix}0 \\{- {lf}_{T_{1}}} \\\tau_{1{}}\end{bmatrix}},\mspace{14mu} {\tau_{3} = {\begin{bmatrix}0 \\{lf}_{T_{3}} \\\tau_{3{}}\end{bmatrix}.}}} & (9)\end{matrix}$

-   -   The components of the aerodynamic drag torque τ_(d) acting to        oppose the multicopter's sense of rotation will be assumed to        act only parallel to z, such that τ_(d)=(0, 0, −τ_(d)) (note the        distinction between the vector τ_(d) and the scalar τ_(d)).

Denoting again the rotation of the body-fixed frame with respect someinertial predefined reference frame 160 with R and the angular velocityof the body with ω^(B), the differential equation of R is as in (1). Theorientation of the multicopter is again described by (3), withassociated differential equation given by (4).

Referring to (5), the angular velocity of rotor i with respect, to themulticopter body, and expressed in the body-fixed frame, is ω^(R) ^(i)=(0, 0, ω^(R) ^(i) ) (note again the distinction between the vectorω^(R) ^(i) and scalar ω^(R) ^(i) ).

The left hand side of (5) contains the angular acceleration, andsimplifies to

$\begin{matrix}{{I^{B}{\overset{.}{\omega}}^{B}} = {\begin{bmatrix}{I_{X}^{B}\overset{.}{p}} \\{I_{Y}^{B}\overset{.}{q}} \\{I_{Z}^{B}\overset{.}{r}}\end{bmatrix}.}} & (10)\end{matrix}$

The orientation of the multicopter is to be controlled through theangular velocity components p and q

The sum of all torques, the first term on the right hand side, containsthe propellers' torque vectors and the aerodynamic drag torque opposingthe multicopter's sense of rotation, and yields

$\begin{matrix}{{\sum\limits_{j}\tau_{j}} = {\begin{bmatrix}0 \\{l\left( {{- f_{T_{1}}} + f_{T_{3}}} \right)} \\{{- \tau_{d}} + \tau_{1{}} + \tau_{3{}}}\end{bmatrix}.}} & (11)\end{matrix}$

The final term of (5) expresses the cross coupling of the angularmomentum in the system, due to taking the derivative in a non-inertialframe

Multiplying out the term, adding the components, and under the previousassumptions given yields

$\begin{matrix}{{{〚{\omega^{B} \times}〛}\mspace{11mu} \left( {{I^{B}\omega^{B}} + {\sum\limits_{i = {\{{1,3}\}}}{I^{R}\left( {\omega^{B} + \omega^{R_{i}}} \right)}}} \right)} \approx {\ldots \mspace{14mu}\begin{bmatrix}{{\left( {I_{Z}^{B} - I_{Y}^{B}} \right){qr}} + {{I_{Z}^{R}\left( {\omega^{R_{1}} + \omega^{R_{3}}} \right)}q}} \\{{{- \left( {I_{Z}^{B} - I_{X}^{B}} \right)}{pr}} - {{I_{Z}^{R}\left( {\omega^{R_{1}} + \omega^{R_{3}}} \right)}p}} \\{\left( {I_{Y}^{B} - I_{X}^{B}} \right)\; {pq}}\end{bmatrix}}} & (12)\end{matrix}$

From the above, writing out (5) in its components yields the threescalar differential equations

I _(X) ^(B) {dot over (p)}=((I _(Y) ^(B) −I _(Z) ^(B))r−I _(Z)^(R)(ω^(R) ¹ +ω^(R) ³ ))q  (13)

I _(Y) ^(B) {dot over (q)}=((I _(Z) ^(B) −I _(X) ^(B))r+I _(Z)^(R)(ω^(R) ¹ +ω^(R) ³ ))p+ . . . (−f _(T) ₁ +f _(T) ₃ )l  (14)

I _(Z) ^(B) {dot over (r)}=(I _(X) ^(B) −I _(Y) ^(B))pq+τ_(1∥)+τ_(3∥)−τ_(d).  (15)

From this can be seen that sending control signals to the propellersallows to directly effect an angular acceleration {dot over (q)} aboutx. Because it has a component perpendicular to the primary axis 130,this directly produced angular acceleration is linearly independent ofthe primary axis 130. Furthermore, through the above mentioned angularacceleration {dot over (q)}, an angular velocity q can be achieved.

Thus, by turning the body through a secondary axis lying along y, themulticopter's angular velocity components about the primary axis 130 (r)and the secondary axis (q) will interact to produce an angularacceleration (and thus a turning) about a turning axis, here x.Important to note is that the secondary axis lies at a non-zero anglewith respect to the primary axis 130 (i.e. is linearly independent ofthe primary axis 130), and that the turning axis lies at a non-zeroangle to both the primary and secondary axes (i.e. the turning axis islinearly independent of both). Concretely, for this multicopter, thismeans that although the rotors can not produce a torque about the xaxis, the component p of angular velocity lying along x can be affected,and the primary axis' 130 orientation with respect to an inertial framecan be controlled. Similarly, for other multicopters, this means thatthe above effect can be actively exploited for their control rather thancounteracted or otherwise compensated for.

Furthermore, this orientation can be maintained by bringing the angularvelocity components p and q to zero, and commanding the propellers suchthat f_(T) ₁ r=f_(T) ₃ such that, {dot over (p)}=0 and {dot over (q)}=0by (13) and (14), respectively. The multicopter's angular velocity willthen point along the primary axis 130 and the orientation will beconstant.

The component of the multicopter's angular velocity along the primaryaxis 130, r, will be dominated by the torques τ_(i∥) and the drag torqueτ_(d). Since the drag torque will typically monotonically increase withr, there will be an imbalance in τ_(1∥)+τ_(3∥)−τ_(d) at low speeds, suchthat the multicopter will increase this component of angular velocity,and thus the multicopter has a natural tendency to rotate about theprimary axis 130. For fixed pitch propellers, there is typically astrongly linear relationship between the magnitude of the thrust forcef_(T) _(i) and the aerodynamic reaction drag torque τ_(i∥).

A translational acceleration of the multicopter can now be effected, byusing the difference of the two forces f_(T) ₁ and f_(T) ₃ to attain andmaintain an orientation of the primary axis, and using the sum of thetwo propeller thrust forces to achieve a resultant force acting on thebody. Specifically, a target thrust force magnitude can be achieved withf_(T) ₁ and f_(T) ₂ .

Note that while the above derivation was made under specificassumptions, these assumptions are reasonable for the derivation ofcontrol schemes for practical multicopter configurations and lead topractical and applicable control schemes. The above results, therefore,hold for a broader range of circumstances and should be interpreted assuch.

The above derivation may be repeated for vehicle's which haveoff-diagonal terms in the inertia matrices. In this case the algebra ismore complicated, but the resulting equations are similar. Likewise, theinertia of the propellers may be comparable to the inertia of the body,or the speed of the propellers comparable to the speed of the body.

Furthermore, given the benefits of the present invention it will bereadily apparent to one skilled in the art that the specific control lawused can vary, and can be derived using linear methods such as thelinear quadratic regulator (LQR), using pole placement, various robustcontrol methods, or nonlinear control methods.

FIG. 5 shows examples of effectors disabled due to a failure 100 for astandard quadrocopter, with all propellers having parallel axes ofrotation, and with propellers opposing one another having the same senseof rotation, and adjacent propellers having the opposite senses ofrotation. Effectors disabled due to a failure are indicated by a large“X” above the concerned effector. Standard multicopter control methodscan not control a multicopter having a failed propeller as they are thenno longer able to independently produce angular accelerations in allaxes.

FIG. 5 (a) shows a quadrocopter with a single propeller completelydisabled by failure. Multicopter control can be regained by applying thedisclosed method, but the multicopter is not controllable using standardmulticopter control.

FIG. 5 (b) shows a quadrocopter with two opposing propellers completelydisabled by a failure. Multicopter control can be regained by applyingthe disclosed method, but the multicopter is not controllable usingstandard multicopter control.

FIG. 5 (c) shows a quadrocopter with two adjacent propellers disableddue to a failure. Multicopter control can be regained by applying thedisclosed method, but the multicopter is not controllable using standardmulticopter control.

FIG. 5 (d) shows a quadrocopter with three propellers disabled due to afailure. Multicopter control can be regained by applying the disclosedmethod, but the multicopter is not controllable using standardmulticopter control.

FIG. 5 (e) shows a quadrocopter with four propellers disabled due to afailure. The quadrocopter is not controllable.

Exemplary Control Architecture

FIG. 6 shows an exemplary implementation of the disclosed method on aflying multicopter, where the method is broken down into an outer 602and an inner 604 control loop. Other implementations of the disclosedmethod will be apparent to those skilled in the arts. A high level goal610 is given by a user and is sent, to a translational controller 612.High level sensors 614, such as GPS sensors and onboard vision systemssend measurements to a translational state estimator 616, whichestimates the multicopter's translational state and sends this estimateto the translational controller. The translational controller generatesa target translational acceleration of the body in order to achieve thehigh level goal.

An attitude controller 642 receives this target translationalacceleration, and sends control signals to each of the propellers 660.This attitude controller 642 computes a target orientation of themulticopter's primary axis 150 and a total commanded force that resultsin the target acceleration; then using the disclosed method, to generatea control signal for each propeller. Sensor measurements are passed to astate estimator 646 which estimates the multicopter's rotation andangular velocity and sends these estimates to the attitude controller.The sensor measurements are obtained from inertial sensors 644, whichmay include accelerometers, rate gyroscopes. Further examples of onboardsensors may include visual sensors such as cameras, range sensors,height sensors and relative airspeed sensors.

FIG. 7 shows alternative layouts of multicopters, with various effectorsdisabled due to failures, all of which are still controllable by usingthe disclosed invention. Specifically, FIG. 7(A) shows a multicopterwith eight effectors, arranged in pairs of two, where two opposing pairsof effectors have completely failed, and wherein the resultingconfiguration is still controllable using the disclosed invention. FIG.7(B) shows a multicopter with eight effectors, arranged symmetricallyabout the centre of mass and with alternating senses of rotation, wherefive adjacent effectors have completely failed, and wherein theresulting configuration is still controllable using the disclosedinvention. FIG. 7(C) shows a multicopter with eight effectors, arrangedin an H-configuration with four effectors on each side, where all fourof the effectors on one side have completely failed, and wherein theresulting configuration is still controllable using the disclosedinvention.

FIG. 8 shows an exemplary flowchart, for deciding control method in caseof a failure on a multicopter. After a failure 802, the system checkswhether it can still produce torques 804. If it cannot, the multicopteris uncontrollable 812. If, however, the multicopter can produce torque,and all torques acting on the body can be made to sum to zero andfurthermore torques can be produced in three independent, directions806, then the multicopter can be controlled using the standardmulticopter control method as known in the prior art. If the standardmulticopter control method cannot be used, then the multicopter canstill be controlled with the disclosed invention 816.

FIG. 9 shows a quadrocopter experiencing a single rotor failure, andutilising the present invention to control the multicopter. Without lossof generality, it is assumed that effectors 1 through 3 are stilloperational, and that effector 4 has been disabled due to a failure 100.Effectors 1 and 3 rotate in the same direction 108 b, while effector 2rotates in the opposite direction 108 a. The thrust forces f_(T) ₁ ,f_(T) ₂ and f_(T) ₃ point in the same direction, along the body z axisas shown in FIG. 9(C), and the respective torque vectors as shown inFIG. 9(B). The imbalance of the torques produced by the propellerscauses the multicopter to rotate with angular velocity ω^(B) such that adrag torque acting on the body τ_(d) acts to balance the propellertorques. The present invention is used to control the multicopter'sangular velocity to lie along the primary axis 130, while a targetorientation of the primary axis 150 with respect to an inertial frame isattained.

In general, the primary axis 130 will no longer lie along z—one methodfor determining the direction of the primary axis 130 is as follows,while referring FIG. 4, and to the notation introduced for FIG. 4. LetI^(B) be the inertia matrix of the multicopter, expressed in the bodyframe, such that

$\begin{matrix}{{I^{B} = \begin{bmatrix}I_{X}^{B} & 0 & 0 \\0 & I_{X}^{B} & 0 \\0 & 0 & I_{Z}^{B}\end{bmatrix}},} & (16)\end{matrix}$

where it has been assumed for simplicity that the inertia matrix isdiagonal and that the multicopter is symmetric such that, the inertiaabout x equals that, about y. The angular momentum of the rotors will beneglected here. Again, ω^(B)=(p, q, r) represents the multicopter body'sangular velocity expressed in the body frame, as shown in FIG. 9(D).

Each rotor i produces a thrust force vector f_(T) _(i) , expressed inthe body frame as f_(T) _(i) =(0, 0, f_(τ) _(i) ). Furthermore, eachrotor i produces a torque vector, passing through the centre of mass120, which are expressed in the body frame as

$\begin{matrix}{{\tau_{1} = \begin{bmatrix}0 \\{- {lf}_{T_{1}}} \\\tau_{z_{1}}\end{bmatrix}},\mspace{14mu} {\tau_{2} = \begin{bmatrix}{lf}_{T_{2}} \\0 \\\tau_{z_{2}}\end{bmatrix}},\mspace{14mu} {\tau_{3} = {\begin{bmatrix}0 \\{lf}_{T_{3}} \\\tau_{z_{3}}\end{bmatrix}.}}} & (17)\end{matrix}$

For simplicity, it will be assumed that the components τ_(z) _(i) areproportional to the thrust force, such that, τ_(z) _(i) =κf_(T) _(i) .An aerodynamic torque τ_(D) is also acting on the body, assumed forsimplicity here to act only in the direction of z, and proportional to rsuch that τ_(D)=(0, 0, −C_(D)r). The differential equation governing theevolution of the body rates can now be written as

I ^(B){dot over (ω)}^(B)=−[[ω^(B) x]]I ^(B)ω+τ₁+τ₂+τ₃+τ_(D)  (18)

which can be expanded and rewritten to yield the following threedifferential equations:

$\begin{matrix}{\overset{.}{p} = {{\frac{I_{X}^{B} - I_{Z}^{B}}{I_{x}^{B}}{qr}} + {\frac{l}{I_{X}^{B}}f_{T_{2}}}}} & (19) \\{\overset{.}{q} = {{{- \frac{I_{X}^{B} - I_{Z}^{B}}{I_{x}^{B}}}{pr}} + {\frac{l}{I_{X}^{B}}\left( {f_{T_{3}} - f_{T_{1}}} \right)}}} & (20) \\{\overset{.}{r} = {{\kappa \left( {f_{T_{1}} - f_{T_{2}} + f_{T_{1}}} \right)} - {C_{D}{r.}}}} & (21)\end{matrix}$

Let n=(n_(x), n_(y), n_(z)) be a unit vector fixed in the inertialframe. This vector evolves according to the differential equation

{dot over (n)}=−[[wx]]n.  (22)

The goal is to now find the set, of commanded forces f_(T) _(i) thatresult in a steady rotational rate ω and a steady n, such that n thendescribes the primary axis 130 expressed in the body frame. This impliesthat {dot over (ω)}=0 and that {dot over (n)}=0. From (22) this impliesthat n=ϵω, where ϵ⁻¹=∥ω∥ such that n is a unit vector.

This yields a set of seven algebraic equations with ten scalar unknownsto solve for (p, q, r, n_(x), n_(y), n_(z), f_(T) ₁ , f_(T) ₂ , f_(T) ₃, ϵ). This can be resolved by adding three additional constraints, forexample: let the first and third effector produce an equal force insteady state, that is

f _(T) ₁ =f _(T) ₃   (23)

and let the second propeller produce half the thrust of the thirdpropeller such that

f _(T) ₂ =f _(T) ₁ /2  (24)

and let, the sum of the thrust forces be such that they can achieve atarget, thrust force magnitude, that balances the weight of themulticopter (mg) when the primary axis 130 points to oppose gravity

(f _(T) ₁ +f _(T) ₂ +f _(T) ₃ )n _(z) =mg.  (25)

This leaves a set of ten algebraic equations in ten unknowns, from whichthe steady-state rotational velocity ω_(B), the direction of the primaryaxis 130 in the body frame n and the steady state thrust forces f_(T)_(i) can be calculated. It is desirable that the thrust forces f_(T)_(i) are relatively large, i.e. far from zero. The present method ofcontrolled flight allows a person skilled in the arts to choose targetsteady state thrust values where the propellers and motors havefavourable characteristics.

A stabilizing controller can now be designed to bring the multicopterfrom some instantaneous angular velocity and orientation to the steadystate solution described above. Furthermore, the orientation of theprimary axis in the inertial frame can be used to translate themulticopter in space.

Note that because the second effector produces significant thrust insteady state f_(T) ₂ >0, the multicopter's centre of mass will not bestationary, but will instead continuously circle about an orbit. Thisbecause the primary axis 130 is not aligned with the direction of theeffector thrusts, such that the component in the direction of gravitycancels out the weight, but the components perpendicular to gravityconstantly cause the multicopter to accelerate to the centre of itsorbit. Thus, when using the above described solution, the multicopter'scentre of mass is unable to remain stationary at a point in space, butwill instead have a continuous motion around this target point in space.

For the case of a quadrocopter having three remaining propellers, analternative strategy would be to disable the one remaining workingpropeller which spins in a different direction from the others, allowingthen the strategy introduced for FIG. 4 to be applied for control.However, this would then require that each propeller must produce halfthe multicopter's weight to maintain the multicopter's altitude, whilewith three propellers the fraction of weight that each remainingpropeller carries will be closer to a third, making this a moreattractive option. The present invention allows a person skilled in thearts to choose either of these two options.

FIG. 10 shows a quadrocopter experiencing three rotor failures, andutilising the present invention to control the multicopter using thesingle remaining propeller. Without loss of generality, it is assumedthat effector 1 is still operational, and that effectors 2, 3 and 4 havebeen disabled by a failure 100. The thrust force f_(T) ₁ , points alongthe body z axis as shown in FIG. 10(C), and the respective torque vectoras shown in FIG. 10(B). The imbalance of the torque produced by thepropeller causes the multicopter to rotate with angular velocity ω_(B)such that a drag torque acting on the body τ_(d) acts to balance thepropeller torques. The present invention is used to control themulticopter's angular velocity to lie along the primary axis 130, whilea target orientation of the primary axis 150 with respect, to aninertial frame is attained.

In general, the primary axis 130 will not lie along z—one method fordetermining the direction of the primary axis 130 is as follows, whilereferring to the notation introduced previously for FIG. 4, and FIG. 4.Let I^(B) be the inertia matrix of the multicopter, expressed in thebody frame, such that

$\begin{matrix}{{I^{B} = \begin{bmatrix}I_{X}^{B} & 0 & 0 \\0 & I_{X}^{B} & 0 \\0 & 0 & I_{Z}^{B}\end{bmatrix}},} & (26)\end{matrix}$

where it has been assumed for simplicity that the inertia matrix isdiagonal and that the multicopter is symmetric such that the inertiaabout x equals that about y. The angular momentum of the rotors will beneglected here. Again, ω^(B)=(p, q, r) represents the multicopter body'sangular velocity expressed in the body frame, as shown in FIG. 10(D).

The rotor produces a thrust force vector f_(T) ₁ , expressed in the bodyframe as f_(T) ₁ =(0, 0, f_(T) ₁ ). Furthermore, the rotor produces atorque vector, passing through the (centre of mass 120, which isexpressed in the body frame as

$\begin{matrix}{{\tau_{1} = \begin{bmatrix}0 \\{- {lf}_{T_{1}}} \\\tau_{z_{1}}\end{bmatrix}},} & (27)\end{matrix}$

For simplicity, it will be assumed that the component τ_(z) ₁ isproportional to the thrust force, such that τ_(z) ₁ =κf_(T) ₁ . Anaerodynamic torque TD is also acting on the body, assumed for simplicityhere to act, only in the direction of z, and proportional to r such thatτ_(D)=(0, 0, −C_(D)τ). The differential equation governing the evolutionof the body rates can now be written as

I ^(B){dot over (ω)}^(B)=−[[ω^(B) x]]I ^(B)ω+τ₁+τ_(D)  (28)

which can be expanded and rewritten to yield the following threedifferential equations:

$\begin{matrix}{\overset{.}{p} = {\frac{I_{X}^{B} - I_{Z}^{B}}{I_{x}^{B}}{qr}}} & (29) \\{\overset{.}{q} = {{{- \frac{I_{X}^{B} - I_{Z}^{B}}{I_{x}^{B}}}{pr}} - {\frac{l}{I_{X}^{B}}f_{T_{1}}}}} & (30) \\{\overset{.}{r} = {{\kappa \; f_{T_{1}}} - {C_{D}{r.}}}} & (31)\end{matrix}$

Let n=(n_(x), n_(y), n_(z)) be a unit vector fixed in a predefinedreference frame 160, taken to be inertial. This vector evolves accordingto the differential equation

{dot over (n)}=−[[wx]]n.  (32)

The goal is to now find the commanded force f_(T) ₁ that results in asteady rotational rate ω and a steady n, such that n then describes theprimary axis 130 expressed in the body frame. This implies that {dotover (ω)}=0 and that, {dot over (n)}=0. From (32) this implies thatn=ϵω, where ϵ⁻¹=∥ω∥ such that n is a unit vector.

This yields a set, of algebraic equations with scalar unknowns to solvefor (p, q, r, n_(x), n_(y), n_(z), f_(T), ϵ). This can be resolved byadding one additional constraint, specifically that the thrust force beable to balance the weight of the multicopter mg:

f _(T) ₁ n _(z) =mg.  (33)

This leaves a set of eight algebraic equations in eight unknowns, fromwhich the steady-state rotational velocity ω^(B), the direction of theprimary axis 130 in the body frame n and the steady state thrust forcef_(T) ₁ can be calculated.

A stabilizing controller can now be designed to bring the multicopterfrom some instantaneous angular velocity and orientation to the steadystate solution described above. Furthermore, the orientation of theprimary axis in the inertial frame can be used to translate themulticopter in space. One method of creating such a controller would beto linearise the equations of motion about the equilibrium, and then doa Linear Quadratic Control synthesis.

The low frequency component of f_(T) ₁ can be used to achieve the targetthrust when averaged over a predefined period, while the high frequencycomponent can be used to control the orientation of the primary axis.

Note that because the effector thrust is not aligned with the gravityvector, the multicopter's centre of mass will not be stationary; butwill instead continuously circle about an orbit. This is because theprimary axis 130 is not aligned with the direction of the effectorthrusts, such that the component in the direction of gravity cancels outthe weight, but the components perpendicular to gravity constantly causethe multicopter to accelerate to the centre of its orbit. Thus, whenusing the above described solution, the multicopter's centre of mass isunable to remain stationary at a point, in space, but will instead havea continuous motion around this target point in space.

Note that, in the preceding, the primary rotation is not necessarilyabout a principle axis of inertia.

It will thus be seen that the objects set forth above, among those madeapparent from the preceding description, are efficiently attained and,because certain changes may be made in carrying out the above method andin the construction(s) set forth without departing from the spirit andscope of the invention, it is intended that all matter contained in theabove description and shown in the accompanying drawings shall beinterpreted as illustrative and not in a limiting sense.

TABLE OF SYMBOLS AND FIGURE NUMERALS Num. Name 100 Effector disabled dueto a failure 102 Effectors 102a Effector 1 102b Effector 2 102c Effector3 102d Effector 4 104 Propellers 106 Motors 108 Direction of propellerrotation 108a Clockwise direction of propeller rotation 108bCounterclockwise direction of propeller rotation 110 Drive axis ofrotation of propeller 112 Multicopter body 114 Mechanical structure 118Direction of sustained multicopter rotation about primary axis 120Center of mass of multicopter 130 Primary axis 140 Quadrocopter 150Target orientation of primary axis 160 Predefined reference frame 302Flight Module 304 Input Unit 306 Control Unit 308 Evaluation Unit 310Sensing Unit 312 Memory Unit 314 Control signal for effectors 602 Outercontrol loop 604 Inner control loop 610 High level goal 612Translational controller 614 High level sensors (e.g. Vision, GPS) 616Translational state estimator 642 Attitude controller 644 Inertialsensors 646 Attitude state estimator 660 Propellers 802 Failure 804 Canthe multicopter produce torque? 806 Torques can be made to sum to zero,and can produce independent torques in all three dimensions? 810 Use thestandard multicopter control method. 812 The multicopter isuncontrollable. 816 Use the disclosed control method. a Targetacceleration f_(des) Target thrust force magnitude f_(D) _(i) Rotor dragforce vectors of rotor i f_(T) _(i) Rotor thrust force vectors of rotori f_(T) _(i) Thrust force for each propeller i g Gravitationalacceleration m Mass of the multicopter mg Weight of the multicopter ñTarget orientation p, q Components of the angular velocity {dot over(p)}, {dot over (q)} Components of the angular acceleration I^(B)Inertia matrix f_(T) _(i) Thrust force vectors I^(B) Inertia matrix ofthe multicopter body I^(R) ^(i) Inertia matrix of propeller i nOrientation of the primary axis R Rotation matrix x, y, z Axes of thecoordinate system τ_(i) Torque vector τ_(i||) Torque vector componentparallel to the primary axis τ_(i⊥) Torque vector componentperpendicular to the primary axis τ_(d) Aerodynamic torque (scalar)τ_(d) Aerodynamic torque (vector) τ_(i) Torque vector of rotor i ω^(B)Angular velocity of the body ω^(V) Angular velocity of the multicopterin an inertial frame ω^(R) ^(i) Angular velocity of rotor i with respectto the multi- copter body (scalar) ω^(R) ^(i) Angular velocity of rotori with respect to the multi- copter body (vector)

1-45. (canceled)
 46. A method for operating a multicopter experiencing afailure during flight, the multicopter comprising, a body; and at leastfour effectors attached to the body, each configured to produce both atorque and a thrust force which can cause the multicopter to fly, themethod comprising the steps of, when a failure has occurred in one ormore of said at least four effectors resulting in a decrease in thetorque and/or the thrust force produced by an effector, determining thedecrease of torque and/or thrust force produced by said effector: usinga control unit to control one or more of said at least four effectors,based on, the determined decrease of torque and/or thrust force producedby said effector, the orientation of a primary axis of said body withrespect to a predefined reference frame, and the angular velocity ofsaid multicopter, such that said one or more effectors collectivelyproduce a torque perpendicular to said primary axis, wherein the torqueperpendicular to said primary axis causes said multicopter to move suchthat the orientation of said primary axis converges to a targetorientation with respect to said predefined reference frame, and suchthat each of said one or more effectors individually produces a thrustforce along said primary axis.
 47. A method according to claim 46comprising a step of identifying the failure that has occurred, andwherein said steps of determining the decrease of torque and/or thrustforce produced by said effector, and, using a control unit to controlone or more of said at least four effectors, are carried out in responseto identifying the failure.
 48. A method according to claim 47 whereinthe step of identifying a failure is carried out using an evaluationunit which can communicate with the control unit.
 49. A method accordingto claim 46 wherein the step of determining the decrease of torqueand/or thrust force produced by said effector is carried out by anevaluation unit which can communicate with the control unit.
 50. Amethod according to claim 47 wherein the step of identifying a failurecomprises identifying a failure which results in a decrease of thetorque and/or thrust force produced by at least one of said effectors byan amount greater than 20%; or wherein the step of identifying a failurecomprises identifying a failure which results in a decrease of thetorque and/or thrust force produced by at least one of said effectors byan amount greater than 50%; or wherein the step of identifying a failurecomprises identifying a failure which results in a decrease of thetorque and/or thrust force produced by at least one of said effectors byan amount greater than 80%.
 51. A method according to claim 47 whereinthe step of identifying a failure comprises identifying a failure whichresults in the a least one of said effectors producing no torque and/orthrust force.
 52. A method according to claim 47 wherein the step ofidentifying a failure, is carried out by an evaluation unit based ondata representative of at least one of: (a) one or more variables of aplurality of variables of the effector, and/or (b) data representativeof the motion of said multicopter.
 53. A method according to claim 52wherein the plurality of variables of the effector comprises at leastone of: rotational speed; voltage; electric current; fuel flow; motortorque; mass flow; and/or power.
 54. A method according to claim 52wherein said data representative of the motion of said multicopter,comprises one or more of: an orientation of said multicopter; an angularvelocity of said multicopter; an operational state of said effectors ofsaid multicopter; an acceleration of said multicopter; a translationalvelocity of said multicopter; and/or a position of said multicopter. 55.A method according to claim 47, wherein in response to said identifyingsaid failure, using a control unit to control one or more of said atleast four effectors, such that said one or more effectors furthercollectively produce a torque along said primary axis, which causes saidmulticopter to rotate about said primary axis.
 56. A method according toclaim 55 wherein said torque along said primary axis causes saidmulticopter to rotate about said primary axis at a speed greater than0.5 revolutions per second.
 57. A method according to claim 46,comprising using the control unit to carry out steps of, computing saidestimate of the orientation of the primary axis of said body withrespect to a predefined reference frame; and computing said estimate ofthe angular velocity of said multicopter.
 58. A method according toclaim 46 wherein said primary axis is an axis aligned with a sum ofthrust forces produced by said one or more of said at least foureffectors over a predefined time with respect to the predefinedreference frame.